Question: Rewrite as a simplified fraction. ${1.7\overline{3} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 173.3333...\\ 10x &= 17.3333...\end{align*}}$ Subtracting the two equations, we have: ${90x = 156}$ ${x = \dfrac{156}{90}} $ ${x = \dfrac{26}{15}} \text{or} {1 \dfrac{11}{15}}$